Recent years witnessed an unprecedented advancement in audio coding technology. This has led to high compression ratios while keeping audible degradation in the compressed signal to a minimum. These coders are intended for a variety of applications, including 5.1 channel film soundtracks, HDTV, laser discs and multimedia. Description of a compression method used in such coders can be found in the ATSC Standard, “Digital Audio Compression (AC-3) Standard”, Document A/52, 20 Dec. 1995.
In the basic approach, at the encoder the time domain signal is sectioned into frames, each frame comprising of a number of blocks. The time domain signal in each block is first converted to the frequency domain using a bank of filters. The frequency domain coefficients, thus generated, are next converted to floating point representation. In floating point syntax, each coefficient is represented as a mantissa and an exponent. The bulk of the compressed bitstream transmitted to the decoder comprises these exponents and mantissas.
The coders are expected to operated in real time. Therefore it is important that the processing at both the encoders and decoders be highly optimised. The ATSC standard outlines a method for conversion of the inverse cosine transform to Fast Fourier Transform to obtain remarkable speed gain.
Frequency transformation presents one of the greatest computation requirements in any transform coder. Therefore, an efficient implementation of this phase can decrease the computation requirement of the system significantly and make real time operation of encoder an easily attainable possibility.
In some encoders such as the AC-3, the frequency domain transformation of signals is performed by the modified discrete cosine transform (MDCT). If directly implemented, the MDCT requires O(N2) additions and multiplications.
However it is possible to reduce the number of required operations significantly if one is able to express the MDCT equation into a form that is amenable to the use of the well known Fast Fourier Transform (FFT) method of J. W. Cooley and J. W. Tukey (1960).
To compute the MDCT of a sequence of N real data, conventional methods use a system comprising of a pre-processing block, an N-point FFT block and finally a post-processing block.